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Different Solution Strategy for Solving Type-2 Fuzzy System of Differential Equations with Application in Arms Race Model

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Abstract

In this article, we have considered a system of type-2 fuzzy differential equation (ST2FDE) to represent Richardson’s arms race model in type-2 fuzzy environment. A novel theorem on the type-2 fuzzy extension principle is presented here and the model has been solved by the \(gH_2\)-differentiability and extension principle techniques with proper numerical illustrations. Four sub-cases were addressed separately for the \(gH_2\)-differentiability. The solution obtained by both methods has been defuzzified using the regular weighted point defuzzification technique. Finally, the idea of the arms race model has been successfully implemented to a real-life problem on advertisement spending of competing mobile companies in the type-2 fuzzy environment.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O. Botanic Garden, Howrah, 711103, West Bengal, India

    Suklal Tudu & Shariful Alam

  2. Department of Applied Science, Maulana Abul Kalam Azad University of Technology, Nadia, 721249, West Bengal, India

    Sankar Prasad Mondal

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  1. Suklal Tudu
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  2. Sankar Prasad Mondal
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  3. Shariful Alam
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Correspondence to Shariful Alam.

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Tudu, S., Mondal, S.P. & Alam, S. Different Solution Strategy for Solving Type-2 Fuzzy System of Differential Equations with Application in Arms Race Model. Int. J. Appl. Comput. Math 7, 177 (2021). https://doi.org/10.1007/s40819-021-01116-0

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